For high-performance lasers with high beam quality (such as CO2, disc, rod, and fiber lasers), the power densities required for deep welding can be achieved with large focal lengths (that is, >about 200 mm), which permits performance of welding processes at large working distances (that is, “remote welding”). In such remote welding processes, which are carried out directly at the processing location without a processing gas (that is, a working gas), the welding results show very large fluctuations in welding depth or root formation in through welds. A through weld is a weld that extends the whole thickness of the workpiece, which can be made of, for example, sheet metal. These fluctuations range from a lack of a through weld with only little developed tempering colors on a rear side of the sheet metal (that is, the workpiece to be welded) to a through weld. These variations in a welding seam have been observed in welding with solid state lasers since disc lasers used together with focusing optics produce a large focal length. The welding seam fluctuations occur, in particular, with F numbers (F number=focal length of the focusing lens/beam diameter on the focusing lens) that are larger than 8.